I'm currently doing an introductory course to quantum mechanics, and came across an assumption that Planck used in solving the UV catastrophe. From what I understand, he essentially stated that that the change in energy cannot be smaller than $hf$. So generally $\Delta{E}$ = $n*hf$ where $n$ is a real number. This makes sense, but I never understood how energy is truly then quantised, as can't light take an infinite number of possible frequencies? (not at the same time but just generally). Maybe I'm just misunderstanding the statement or making it overcomplicated - in any case please do shed some light.
$\begingroup$
$\endgroup$
2
-
2$\begingroup$ Possible duplicate: physics.stackexchange.com/q/472450 $\endgroup$– Nihar KarveCommented Jun 12, 2021 at 9:19
-
$\begingroup$ Light may have many different frequencies, but for every particular frequency $f$ the energy is emitted in quanta of size $hf$. $\endgroup$– Roger V.Commented Jun 12, 2021 at 9:22
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
The crucial insight made by quantum mechanics is that electromagnetic waves in the cavity can be described by simple harmonic oscillators. If the angular frequency of the mode of oscillation is $\omega $ (FIXED) , then the energy associated with this mode is given by $$E_n=\hbar \omega \left(n+\frac{1}{2}\right)\ \ \ \ \ n=0,1,2,\cdots $$ which are quantized.
NOTE that we are looking at a particular mode of frequency, not the whole spectrum.
